BNPmix provides a set of functions for density estimation with Dirichlet process and Pitman–Yor mixing measures via marginal algorithms.
DPpackage is a more general purpose package than both BNPdensity and BNPmix, including functions for regression models, generalised linear mixed models, and generalised additive models, on top of the density model. However, the implementation is primarily tailored to the Dirichlet process mixing measure.
A natural extension to the Dirichlet and Pitman–Yor processes are Gibbs-type priors [1]}. NRMI are large classes of priors than Gibbs-type priors, and their intersection is identified by the NGG process considered in BNPdensity, as established in [2]}. Being an extremely general class of priors, Gibbs-type processes are beyond reach for a general treatment in a software, however both BNPdensity and BNPmix packages cover its most commonly used sub-classes.
Pitman–Yor process is not implemented in BNPdensity as it is not an NRMI; yet, a dependence to BNPmix is made in BNPdensity, in such a way that users interested in comparing their results with Pitman–Yor can also use the dedicated functions MixPY1 (semiparametric) and MixPY2 (fully nonparametric) that call BNPmix PYdensity function.
The mixing measures covered by the three packages and their mutual relationships are illustrated in Figure REF .
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